Comprehensive NEET Chemistry Notes: The Solid State

1. Key Formulae in The Solid State

1.1 Number of Atoms in a Unit Cell

• Simple Cubic Unit Cell (Primitive):
• • Number of atoms per unit cell: $1\text{ atom}$
  • Explanation: Atoms are located only at the corners of the cube. Each atom at a corner is shared among 8 unit cells.
  • Derivation: Since there are 8 corners and each contributes $\frac{1}{8}$ to a unit cell, the total number of atoms is $8\times \frac{1}{8}=1$.
• Body-Centred Cubic (BCC) Unit Cell:
• • Number of atoms per unit cell: $2\text{ atoms}$
  • Explanation: Atoms are located at the 8 corners and one atom is at the body center.
  • Derivation: The body-centered atom is not shared with any other unit cell, contributing fully, while the 8 corner atoms contribute $\frac{1}{8}$ each.
• Face-Centred Cubic (FCC) Unit Cell:
• • Number of atoms per unit cell: $4\text{ atoms}$
  • Explanation: Atoms are located at the 8 corners and at the centers of the 6 faces.
  • Derivation: Each face-centered atom is shared between 2 unit cells, contributing $\frac{1}{2}$ to a unit cell, and the 8 corner atoms contribute $\frac{1}{8}$ each.

1.2 Packing Efficiency

• Packing Efficiency of FCC and HCP Structures:
• • Formula: $\text{Packing Efficiency}=\frac{\text{Volume occupied by atoms in unit cell}}{\text{Total volume of unit cell}}\times 100$
  • For FCC and HCP: $\text{Packing Efficiency}=74$
  • Explanation: In both FCC and HCP, the packing efficiency is the highest due to the effective use of space with each atom surrounded by 12 others.
• Packing Efficiency of BCC Structure:
• • Formula: $\text{Packing Efficiency}=\frac{\text{Volume occupied by atoms in unit cell}}{\text{Total volume of unit cell}}\times 100$
  • For BCC: $\text{Packing Efficiency}=68$
  • Explanation: The BCC structure, while more efficient than the simple cubic, is less efficient than FCC or HCP.
• Packing Efficiency of Simple Cubic Structure:
• • Formula: $\text{Packing Efficiency}=\frac{\text{Volume occupied by atoms in unit cell}}{\text{Total volume of unit cell}}\times 100$
  • For Simple Cubic: $\text{Packing Efficiency}=52.4$
  • Explanation: This is the least efficient packing, with significant unoccupied space within the structure.

1.3 Density and Atomic Mass Calculations

• Density Formula:
• • $d=\frac{z\times M}{a^3\times N_A}$
  • Where:
  • • $d$ = Density of the unit cell
    • $z$ = Number of atoms in the unit cell
    • $M$ = Molar mass of the element
    • $a$ = Edge length of the unit cell
    • $N_A$ = Avogadro's number
• Example Application:
• • Given: A BCC unit cell with an edge length of 288 pm and a density of 7.2 g/cm³. Calculate the atomic mass.
  • Solution: Using the formula above, input the values and solve for $M$.

1.4 Defects in Solids

• Schottky Defect:
• • Explanation: Equal numbers of cations and anions are missing from the lattice. It decreases the density of the solid.
  • Common Example: NaCl, KCl.
• Frenkel Defect:
• • Explanation: A cation leaves its normal site and occupies an interstitial site. It does not affect the density.
  • Common Example: AgCl, ZnS.

1.5 Electrical Properties of Solids

• Conduction in Metals:
• • Explanation: Metals have overlapping conduction and valence bands, allowing electrons to move freely, which facilitates conductivity.
• Semiconductors:
• • Types: n-type (electron-rich) and p-type (electron-deficient).
  • Explanation: Small energy gaps allow electrons to move to the conduction band under certain conditions, enhancing conductivity.

Quick Recap

• Simple, BCC, and FCC unit cells differ in the number of atoms they contain and their packing efficiencies.
• The density of a unit cell can be calculated using the relationship between the atomic mass, the number of atoms in a unit cell, and the unit cell's volume.
• Defects in solids such as Schottky and Frenkel defects influence the properties of ionic compounds.
• Conductivity in solids varies greatly, with metals being good conductors and semiconductors requiring doping to improve conductivity.

Practice Questions

1. Calculate the packing efficiency of a BCC unit cell with an edge length of 300 pm.
2. A compound has a cubic unit cell with a density of 8.96 g/cm³ and an edge length of 360 pm. Calculate the molar mass of the compound.
3. Explain how Frenkel and Schottky defects affect the physical properties of ionic solids.
4. Compare the electrical conductivity of metals, semiconductors, and insulators.

This summary provides the key formulae, explanations, and derivations relevant to the chapter on "The Solid State" from the NCERT Chemistry textbook, focusing on areas crucial for NEET preparation.